Inner product computation for sparse iterative solvers on\ud distributed supercomputer

Recent years have witnessed that iterative Krylov methods without re-designing are not suitable for distribute supercomputers because of intensive global communications. It is well accepted that re-engineering Krylov methods for prescribed computer architecture is necessary and important to achieve higher performance and scalability. The paper focuses on simple and practical ways to re-organize Krylov methods and improve their performance for current heterogeneous distributed supercomputers. In construct with most of current software development of Krylov methods which usually focuses on efficient matrix vector multiplications, the paper focuses on the way to compute inner products on supercomputers and explains why inner product computation on current heterogeneous distributed supercomputers is crucial for scalable Krylov methods. Communication complexity analysis shows that how the inner product computation can be the bottleneck of performance of (inner) product-type iterative solvers on distributed supercomputers due to global communications. Principles of reducing such global communications are discussed. The importance of minimizing communications is demonstrated by experiments using up to 900 processors. The experiments were carried on a Dawning 5000A, one of the fastest and earliest heterogeneous supercomputers in the world. Both the analysis and experiments indicates that inner product computation is very likely to be the most challenging kernel for inner product-based iterative solvers to achieve exascale

Minimizing synchronizations in sparse iterative solvers for distributed supercomputers

Eliminating synchronizations is one of the important techniques related to minimizing communications for modern high performance computing. This paper discusses principles of reducing communications due to global synchronizations in sparse iterative solvers on distributed supercomputers. We demonstrates how to minimizing global synchronizations by rescheduling a typical Krylov subspace method. The benefit of minimizing synchronizations is shown in theoretical analysis and is verified by numerical experiments using up to 900 processors. The experiments also show the communication complexity for some structured sparse matrix vector multiplications and global communications in the underlying supercomputers are in the order P1/2.5 and P4/5 respectively, where P is the number of processors and the experiments were carried on a Dawning 5000A

Consequences of 't Hooft's Equivalence Class Theory and Symmetry by Large Coarse Graining

According to 't Hooft (Class.Quantum.Grav. 16 (1999), 3263), quantum gravity can be postulated as a dissipative deterministic system, where quantum states at the ``atomic scale''can be understood as equivalence classes of primordial states governed by a dissipative deterministic dynamics law at the ``Planck scale''. In this paper, it is shown that for a quantum system to have an underlying deterministic dissipative dynamics, the time variable should be discrete if the continuity of its temporal evolution is required. Besides, the underlying deterministic theory also imposes restrictions on the energy spectrum of the quantum system. It is also found that quantum symmetry at the ``atomic scale'' can be induced from 't Hooft's Coarse Graining classification of primordial states at the "Planck scale".Comment: 12 papge, Late

Improved processing of microarray data using image reconstruction techniques

Spotted cDNA microarray data analysis suffers from various problems such as noise from a variety of sources, missing data, inconsistency, and, of course, the presence of outliers. This paper introduces a new method that dramatically reduces the noise when processing the original image data. The proposed approach recreates the microarray slide image, as it would have been with all the genes removed. By subtracting this background recreation from the original, the gene ratios can be calculated with more precision and less influence from outliers and other artifacts that would normally make the analysis of this data more difficult. The new technique is also beneficial, as it does not rely on the accurate fitting of a region to each gene, with its only requirement being an approximate coordinate. In experiments conducted, the new method was tested against one of the mainstream methods of processing spotted microarray images. Our method is shown to produce much less variation in gene measurements. This evidence is supported by clustering results that show a marked improvement in accuracy

Localization of Macroscopic Object Induced by the Factorization of Internal Adiabatic Motion

To account for the phenomenon of quantum decoherence of a macroscopic object, such as the localization and disappearance of interference, we invoke the adiabatic quantum entanglement between its collective states(such as that of the center-of-mass (C.M)) and its inner states based on our recent investigation. Under the adiabatic limit that motion of C.M dose not excite the transition of inner states, it is shown that the wave function of the macroscopic object can be written as an entangled state with correlation between adiabatic inner states and quasi-classical motion configurations of the C.M. Since the adiabatic inner states are factorized with respect to each parts composing the macroscopic object, this adiabatic separation can induce the quantum decoherence. This observation thus provides us with a possible solution to the Schroedinger cat paradoxComment: Revtex4,23 pages,1figur

Robust synchronization for 2-D discrete-time coupled dynamical networks

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini–Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008 and 61174136, the International Science and Technology Cooperation Project of China under Grant No. 2009DFA32050, the Natural Science Foundation of Jiangsu Province of China under Grant BK2011598, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany